After migrating from one computer to another, my iPhone now automatically appears under the devices list in iTunes on both my old and new Macs. I don't want to accidentally sync my iPhone with my old computer. Is there a way I can make it forget it knows my iPhone?

I've tried:

Turning off wifi sync on the old computer, but this is a device-level setting, so as soon as you turn it back on on the new computer, the iPhone shows on both.

On the old computer, deleting all device backups, 'ejecting' the iPhone from iTunes, and forgetting all remotes. None of those measures has had an effect.

If you go to the iTunes > Preferences menu and select the Devices tab you can delete backup's from particular iPhones. Also you can go to iTunes > Preferences > Devices, and check the box 'Prevent iPods. iPhones, and iPads from synching automatically'.